Hi Anna, There are a few reasons: 1. Not all wavelengths of light may pass through lenses. For example, infrared is easily absorbed by glass lenses, so we can't use them to take infrared pictures. Images of different wavelengths are useful for understanding temperature of stars or different objects in a galaxy etc. read more
Mirrors do not split up light this way so telescopes using mirrors will not have chromatic aberration, which means they can be used to produce clearer pictures than a simple telescope using lenses. Another reason why telescopes, especially large ones will use mirrors instead of lenses is because large lenses are heavy, which creates an upper limit for their size before they cannot support their own weight. read more
Because reflecting telescopes are easier to design, build, and maintain than refracting instruments. read more